Stock, Implied, Local Volatilities and Black Scholes Pricing

In this paper we present a critical point on connections between stock volatility, implied volatility, and local volatility. The essence of the Black Sholes pricing model is based on assumption that option piece is formed by no arbitrage portfolio. Such assumption effects the change of the real underlying stock by its risk neutral counterpart. Market practice shows even more. The volatility of the underlying should be also changed. Such practice calls for implied volatility. Underlying with implied volatility is specific for each option. The local volatility development presents the value of implied volatility